2026 · Q11
If 1/(x+k) + 1/(x+2k) + 1/(x+5k) = 1/k, then which one of the following is the solution of this equation?
Elementary MathematicsAlgebra
- Ak/3
- Bk/2
- C2k/3
- Dk
Explanation
Test the candidate x = k directly: 1/(k + k) + 1/(k + 2k) + 1/(k + 5k) = 1/(2k) + 1/(3k) + 1/(6k) = (3 + 2 + 1)/(6k) = 6/(6k) = 1/k. This satisfies the given equation exactly, so x = k is a solution, option D. None of the other candidates (k/3, k/2, 2k/3) reduces the three fractions to a sum of 1/k.